s- and d-wave Symmetries in Nonadiabatic Theory of Superconductivity

High-$T_c$ superconductors have Fermi energies $E_F$ much smaller than conventional metals comparable to phonon frequencies. In such a situation nonadiabatic effects are important. A generalization of Eliashberg theory in the nonadiabatic regime has previously been shown to reproduce some anomalous features of the high-$T_c$ superconductors as for istance the enhancement of $T_c$ or the isotopic effects on $T_c$ and $m^*$. In this contribution we address the issue of the symmetry of the gap in the context of nonadiabatic superconductivity. We show that vertex corrections have a momentum structure which favours d-wave superconductivity when forward scattering is predominant. An additional increase of $T_c$ is also found.Comment: 6 pages, 3 eps figure, ijmpb-macros, proceeding of SATT10, to appear on Int. Journ. Mod. Phys.

Isotope effects in the Hubbard-Holstein model within dynamical mean-field theory

We study the isotope effects arising from the coupling of correlated electrons with dispersionless phonons by considering the Hubbard-Holstein model at half-filling within the dynamical mean-field theory. In particular we calculate the isotope effects on the quasi-particle spectral weight $Z$, the renormalized phonon frequency, and the static charge and spin susceptibilities. In the weakly correlated regime $U/t \lesssim 1.5$, where $U$ is the Hubbard repulsion and $t$ is the bare electron half-bandwidth, the physical properties are qualitatively similar to those characterizing the Holstein model in the absence of Coulomb repulsion, where the bipolaronic binding takes place at large electron-phonon coupling, and it reflects in divergent isotope responses. On the contrary in the strongly correlated regime $U/t \gtrsim 1.5$, where the bipolaronic metal-insulator transition becomes of first order, the isotope effects are bounded, suggesting that the first order transition is likely driven by an electronic mechanism, rather then by a lattice instability. These results point out how the isotope responses are extremely sensitive to phase boundaries and they may be used to characterize the competition between the electron-phonon coupling and the Hubbard repulsion.Comment: 10 pages, 8 figures. The paper has been already accepted on Phys. Rev.

Relevance of multiband Jahn-Teller effects on the electron-phonon interaction in A3A_3C60_{60}

Assessing the effective relevance of multiband effects in the fullerides is of fundamental importance to understand the complex superconducting and transport properties of these compounds. In this paper we investigate in particular the role of the multiband effects on the electron-phonon (el-ph) properties of the $t_{1u}$ bands coupled with the Jahn-Teller intra-molecular $H_g$ vibrational modes in the C$_{60}$ compounds. We show that, assuming perfect degeneracy of the electronic bands, vertex diagrams arising from the breakdown of the adiabatic hypothesis, are one order of magnitude smaller than the non-crossing terms usually retained in the Migdal-Eliashberg (ME) theory. These results permit to understand the robustness on ME theory found by numerical calculations. The effects of the non degeneracy of the $t_{1u}$ in realistic systems are also analyzed. Using a tight-binding model we show that the el-ph interaction is mainly dominated by interband scattering within a single electronic band. Our results question the reliability of a degenerate band modeling and show the importance of these combined effects in the $A_3$C$_{60}$ family.Comment: 5 pages, 3 eps figure

Donor-strand exchange in chaperone-assisted pilus assembly revealed in atomic detail by molecular dynamics

Adhesive multi-subunit fibres are assembled on the surface of many pathogenic bacteria via the chaperone-usher pathway. In the periplasm, a chaperone donates a β-strand to a pilus subunit to complement its incomplete immunoglobulin-like fold. At the outer membrane, this is replaced with a β-strand formed from the N-terminal extension (Nte) of an incoming pilus subunit by a donorstrand exchange (DSE) mechanism. This reaction has previously been shown to proceed via a concerted mechanism, in which the Nte interacts with the chaperone:subunit complex before the chaperone has been displaced, forming a ternary intermediate. Thereafter, the pilus and chaperone β-strands have been postulated to undergo a strand swap by a ‘zip-in-zip-out’ mechanism, whereby the chaperone strand zips out, residue by residue, as the Nte simultaneously zips in. Here, molecular dynamics simulations have been used to probe the DSE mechanism during formation of the Salmonella enterica Saf pilus at an atomic level, allowing the direct investigation of the zip-inzip- out hypothesis. The simulations provide an explanation of how the incoming Nte is able to dock and initiate DSE due to inherent dynamic fluctuations within the chaperone:subunit complex. The chaperone donor-strand is shown to unbind from the pilus subunit residue by residue, in direct support of the zip-in-zip-out hypothesis. In addition, an interaction of a residue towards the Nterminus of the Nte with a specific binding pocket (P*) on the adjacent pilus subunit is shown to stabilise the DSE product against unbinding, which also proceeds by a zippering mechanism. Together, the study provides an in-depth picture of DSE, including the first insights into the molecular events occurring during the zip-in-zip-out mechanism

Assessment of ab initio models of protein complexes by molecular dynamics.

Determining how proteins interact to form stable complexes is of crucial importance, for example in the development of novel therapeutics. Computational methods to determine the thermodynamically stable conformation of complexes from the structure of the binding partners, such as RosettaDock, might potentially emerge to become a promising alternative to traditional structure determination methods. However, while models virtually identical to the correct experimental structure can in some cases be generated, the main difficulty remains to discriminate correct or approximately correct models from decoys. This is due to the ruggedness of the free-energy landscape, the approximations intrinsic in the scoring functions, and the intrinsic flexibility of proteins. Here we show that molecular dynamics simulations performed starting from a number top-scoring models can not only discriminate decoys and identify the correct structure, but may also provide information on an initial map of the free energy landscape that elucidates the binding mechanism

Computational Modeling of Designed Ankyrin Repeat Protein Complexes with their Targets

Recombinant therapeutic proteins are playing an ever-increasing role in the clinic. High-affinity binding candidates can be produced in a high-throughput manner through the process of selection and evolution from large libraries, but the structures of the complexes with target protein can only be determined for a small number of them in a costly, low-throughput manner, typically by x-ray crystallography. Reliable modeling of complexes would greatly help to understand their mode of action and improve them by further engineering, for example, by designing bi-paratopic binders. Designed ankyrin repeat proteins (DARPins) are one such class of antibody mimetics that have proven useful in the clinic, in diagnostics and research. Here we have developed a standardized procedure to model DARPin–target complexes that can be used to predict the structures of unknown complexes. It requires only the sequence of a DARPin and a structure of the unbound target. The procedure includes homology modeling of the DARPin, modeling of the flexible parts of a target, rigid body docking to ensembles of the target and docking with a partially flexible backbone. For a set of diverse DARPin–target complexes tested it generated a single model of the complex that well approximates the native state of the complex. We provide a protocol that can be used in a semi-automated way and with tools that are freely available. The presented concepts should help to accelerate the development of novel bio-therapeutics for scaffolds with similar properties

The Role of High-Dimensional Diffusive Search, Stabilization, and Frustration in Protein Folding

Proteins are polymeric molecules with many degrees of conformational freedom whose internal energetic interactions are typically screened to small distances. Therefore, in the high-dimensional conformation space of a protein, the energy landscape is locally relatively flat, in contrast to low-dimensional representations, where, because of the induced entropic contribution to the full free energy, it appears funnel-like. Proteins explore the conformation space by searching these flat subspaces to find a narrow energetic alley that we call a hypergutter and then explore the next, lower-dimensional, subspace. Such a framework provides an effective representation of the energy landscape and folding kinetics that does justice to the essential characteristic of high-dimensionality of the search-space. It also illuminates the important role of nonnative interactions in defining folding pathways. This principle is here illustrated using a coarse-grained model of a family of three-helix bundle proteins whose conformations, once secondary structure has formed, can be defined by six rotational degrees of freedom. Two folding mechanisms are possible, one of which involves an intermediate. The stabilization of intermediate subspaces (or states in low-dimensional projection) in protein folding can either speed up or slow down the folding rate depending on the amount of native and nonnative contacts made in those subspaces. The folding rate increases due to reduced-dimension pathways arising from the mere presence of intermediate states, but decreases if the contacts in the intermediate are very stable and introduce sizeable topological or energetic frustration that needs to be overcome. Remarkably, the hypergutter framework, although depending on just a few physically meaningful parameters, can reproduce all the types of experimentally observed curvature in chevron plots for realizations of this fold

Bioorthogonal Double-Fluorogenic Siliconrhodamine Probes for Intracellular Superresolution Microscopy

A series of double-fluorogenic siliconrhodamine probes were synthesized. These tetrazine-functionalized, membrane-permeable labels allowed site-specific bioorthogonal tagging of genetically manipulated intracellular proteins and subsequent imaging using super-resolution microscopy

Gating of TonB-dependent transporters by substrate-specific forced remodelling

Membrane proteins play vital roles in inside-out and outside-in signal transduction by responding to inputs that include mechanical stimuli. Mechanical gating may be mediated by the membrane or by protein(s) but evidence for the latter is scarce. Here we use force spectroscopy, protein engineering and bacterial growth assays to investigate the effects of force on TonB-TonB dependent transporter (TBDT) complexes of Gram-negative bacteria. We confirm the feasibility of protein-only mediated mechanical gating by demonstrating that the interaction between TonB and BtuB (a TBDT) is sufficiently strong under force to create a channel through the TBDT. In addition, by comparing the dimensions of the force-induced channel in BtuB and a second TBDT (FhuA) we show that the mechanical properties of the interaction are perfectly tuned to their function by inducing formation of a channel whose dimensions are tailored to the ligand

Protein mechanics probed using simple molecular models

Background: Single-molecule experimental techniques such as optical tweezers or atomic force microscopy are a direct probe of the mechanical unfolding/folding of individual proteins. They are also a means to investigate free energy landscapes. Protein force spectroscopy alone provides limited information; theoretical models relate measurements to thermodynamic and kinetic properties of the protein, but do not reveal atomic level information. By building a molecular model of the protein and probing its properties through numerical simulation, one can gauge the response to an external force for individual interatomic interactions and determine structures along the unfolding pathway. In combination, single-molecule force probes and molecular simulations contribute to uncover the rich behavior of proteins when subjected to mechanical force. Scope of review: We focus on how simplified protein models have been instrumental in showing how general properties of the free energy landscape of a protein relate to its response to mechanical perturbations. We discuss the role of simple protein models to explore the complexity of free energy landscapes and highlight important conceptual issues that more chemically accurate models with all-atom representations of proteins and solvent cannot easily address. Major conclusions: Native-centric, coarse-grained models, despite simplifications in chemical detail compared to all-atom models, can reproduce and interpret experimental results. They also highlight instances where the theoretical framework used to interpret single-molecule data is too simple. However, these simple models are not able to reproduce experimental findings where non-native contacts are involved. General significance: Mechanical forces are ubiquitous in the cell and it is increasingly clear that the way a protein responds to mechanical perturbation is important